Information on Result #1653615
Linear OOA(2257, 1679085, F2, 5, 19) (dual of [(1679085, 5), 8395168, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(249, 1365, F2, 5, 9) (dual of [(1365, 5), 6776, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(249, 1365, F2, 3, 9) (dual of [(1365, 3), 4046, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(249, 4095, F2, 9) (dual of [4095, 4046, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(249, 4096, F2, 9) (dual of [4096, 4047, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(249, 4096, F2, 9) (dual of [4096, 4047, 10]-code), using
- OOA 3-folding [i] based on linear OA(249, 4095, F2, 9) (dual of [4095, 4046, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(249, 1365, F2, 3, 9) (dual of [(1365, 3), 4046, 10]-NRT-code), using
- linear OOA(2208, 1677720, F2, 5, 19) (dual of [(1677720, 5), 8388392, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2257, 1679085, F2, 6, 19) (dual of [(1679085, 6), 10074253, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2257, 1679085, F2, 7, 19) (dual of [(1679085, 7), 11753338, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(2257, 1679085, F2, 8, 19) (dual of [(1679085, 8), 13432423, 20]-NRT-code) | [i] | ||
| 4 | Digital (238, 257, 1679085)-net over F2 | [i] | ||